Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

by
Knight, Randall D.

Published by
Pearson

ISBN 10:
0321740904

ISBN 13:
978-0-32174-090-8

Chapter 13 - Newton's Theory of Gravity - Conceptual Questions: 2

Answer

The ratio $\frac{F_1}{F_2}$ is 2

Work Step by Step

Let $M_s$ be the mass of the star.
Let $M$ be the mass of planet 1.
Let $R$ be the distance from the star to planet 1.
We can write an expression for the gravitational force of the star on planet 1.
$F_1 = \frac{G~M_s~M}{R^2}$
Note that the mass of planet 2 is $2M$ and the distance from the star to planet 2 is $2R$. We can write an expression for the gravitational force of the star on planet 2.
$F_2 = \frac{G~M_s~(2M)}{(2R)^2}$
$F_2 = \frac{G~M_s~M}{2~R^2}$
$F_2 = \frac{F_1}{2}$
We can divide $F_1$ by $F_2$.
$\frac{F_1}{F_2} = \frac{F_1}{(F_1/2)} = 2$
The ratio $\frac{F_1}{F_2}$ is 2.